If the roots of the equation x² + px + 12 = 0 are 3 and 4, what is the value of

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Question: If the roots of the equation x² + px + 12 = 0 are 3 and 4, what is the value of p? (2020)

Options:

Correct Answer: -7

Exam Year: 2020

Solution:

The sum of the roots is -p = 3 + 4 = 7, hence p = -7.

If the roots of the equation x² + px + 12 = 0 are 3 and 4, what is the value of p? (2020)

If the roots of the equation x² + px + 12 = 0 are 3 and 4, what is the value of p? (2020)

Step 1: Identify the given quadratic equation, which is x² + px + 12 = 0.
Step 2: Note that the roots of the equation are given as 3 and 4.
Step 3: Use the formula for the sum of the roots of a quadratic equation, which is -p = root1 + root2.
Step 4: Substitute the values of the roots into the formula: -p = 3 + 4.
Step 5: Calculate the sum of the roots: 3 + 4 = 7.
Step 6: Now we have -p = 7. To find p, we need to solve for p.
Step 7: Multiply both sides of the equation by -1 to get p: p = -7.

Quadratic Equations – Understanding the relationship between the coefficients and the roots of a quadratic equation, specifically using Vieta's formulas.
Vieta's Formulas – Using the sum and product of the roots to find unknown coefficients in a polynomial equation.